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b) Quite possibly is a shortcut for $Hom$. Sometimes the letter $y$ is used (for Yoneda). The trouble is when you are considering the representable functor defined over several categories, e.g. a category and a subcategory.

Bonus: If you, instead of considering contravariant functors $\mathrm{Sch}^{o} \to \mathrm{Set}$, use covariant functors $\mathrm{Aff} \to \mathrm{Set}$ the notation used in EGA is $h_X^{o}$. Perhaps the reason is that Yoneda's map is contravariant in this case.

Of course the notation $h_X$ is used extensively in EGA, but where can you find evidence that that it is Grothendieck's invention?
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Martin BrandenburgFeb 2 '11 at 10:53

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Further evidence: The notation is already on SGA 3 and 4. There are several exposés by Grothendieck in Henri Cartan's seminar from 1960/61 in which he explains his point of view of Teichmüller's space through representable functors in the analytical category and he uses the notation $h_X$. I don't think anyone else was using these ideas at that time. Cartan's seminar is available at numdam.org.
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Leo AlonsoFeb 2 '11 at 11:16